Fiqh-us-Sunnah Volume 1, Purification and Prayer, Fiqh 1.006C.

This refers to animals which die from “natural causes,” that is, without the proper Islamic way of slaughtering. It also includes anything that is cut off of a live animal. Abu Waqid al-Laithy reported that the Prophet, upon whom be peace, said, “What is cut off of a live animal is considered dead,” i.e., it is considered like an animal that has not been properly slaughtered. This is related by Abu Dawud and by at-Tirmizhi, who classifies it as hassan and says that the scholars act according to this hadith.